Then you are active, so the passive DI is good. Your high end will be affected (or not) by the preamp, not the DI.
That's what I've always figured. Before I got my own JDI though I plugged straight into lots of provided ones and never noticed any roll off...but then I wasn't specifically listening for it either. It's only in the last ten years or so that I've started to be more interested in different DI's. For most of my life I've just let it be the sound man's problem. In my "day gig" I work with some great sound men and I'm gonna start pestering them for advice. It's kinda sad that for 30 years or so I've ignored the one piece of gear (besides the bass itself) that's most responsible for my sound out front. Slow learner.